it has a population of more than 10 million people = more than 10 million people live there

If you omit "of", the sentence fails because "more" is not an adjective. If you replace "more" with an adjective like "larger" then the sentence works without "of": "This country has a population larger than 10 million people"

It sounds very natural. My guess is that it would be "population of [people]", but it's perfectly fine to say "population of #." In that case, it's a fancier way of saying "The population is #".

Why did the writer use ‘of’ … There are several perfectly natural ways to express the idea including omitting the ‘of’. … of more than … … that is more than … … more than … I’d rank them in the order above - ‘of’ sounds slightly better.

I agree with Jonathon. This is a pretty common construction you might want to learn about. The table has a weight of 100 kg. The car has a speed of 200 km/hr. The plane has a capacity of 200 people.